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%I #16 Feb 24 2021 09:08:27
%S 2,7,18,25,32,59,71,81,103,135
%N Maximum length of perfect rulers that can be made from segments not exceeding n.
%C We conjecture the extension a(8)=81. For nomenclature related to perfect and optimal rulers see Peter Luschny's "Perfect Rulers" web pages.
%H Peter Luschny, <a href="http://www.luschny.de/math/rulers/introe.html">Perfect and Optimal Rulers.</a> A short introduction.
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/scimath/diffset/consdifs.txt">Largest and smallest maximum differences of consecutive marks of perfect rulers.</a>
%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="https://dx.doi.org/10.21227/cd4b-nb07">MRLA search results and source code</a>, Nov 6 2020.
%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="https://doi.org/10.1109/OJAP.2020.3043541">Large Minimum Redundancy Linear Arrays: Systematic Search of Perfect and Optimal Rulers Exploiting Parallel Processing</a>, IEEE Open Journal of Antennas and Propagation, 2 (2021), 79-85.
%H <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>
%e The complete list of these rulers starts:
%e n.a(n)..rulers
%e 1..2....[0,1,2]
%e 2..7....[0,1,3,5,7]
%e 3.18....[0,1,4,7,10,13,16]
%e 4.25....[0,1,2,6,10,13,17,21,25]
%e ........[0,1,2,6,10,14,17,21,25]
%e ........[0,1,2,6,10,14,18,21,25]
%e ........[0,1,3,7,11,15,19,23,25]
%e 5.37....[0,1,2,3,8,13,18,23,28,33,37]
%e 6.59....[0,1,4,10,16,22,28,34,40,46,52,54,57,59]
%Y Cf. A104307 Least maximum of differences between consecutive marks, A104309 minimum length of perfect rulers containing a segment of length n, A103294 definitions related to complete rulers.
%K hard,more,nonn
%O 1,1
%A _Hugo Pfoertner_, Mar 01 2005
%E Conjectured a(8) proven via exhaustive search and a(9) ... a(10) added by Fabian Schwartau, _Yannic Schröder_, Lars Wolf, Joerg Schoebel, Feb 23 2021
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